[SPOILERS MAIN] If Arya was also captured along with Sansa, Joffrey would have targeted her more

In the books, the biggest reason Joffrey hated Sansa was because of Arya defending herself against him at the trident and if Joffrey managed to get his hands on Arya along with Sansa, Aryas fate would have been much worse.

Firstly, they might not immediately kill her since shes still a Stark but beyond that, I don't think there was anyone in the palace that would have an agenda that required them protect her.

I think it would have been almost a Ramsay and Reek situation with the near absolute power Joffrey had and Cerseis hatred for Arya as well, along with the fact that Sansa is considered the prettier sibling by the Lannisters and Little finger would only be interested in creeping on Sansa.

Even Sansa herself would probably hesitate to step in since she supported Joffrey even after he tried to murder Arya in a long as scene in her chapter, seriously it was so much worse in the books the way he tried chopping off her head whilst she was unarmed and Sansa would also understand that Arya being the focus of Joffreys ire would have meant he would be less focused on her.

Mind you, this was also the point in the story where Tyrion was still outside the city and would have also been less likely to step in.

I think the only other alternative is this, after keeping Ned in the black cells for a week or so, they would have had him and both girls at the sept of Baelor where Joffrey at the spur of the moment has Arya executed in his place and has Sansa as a deterrent for any further reaction but also as punishment.

I genuinely don't think that Arya would have had the same situation at kingslanding because of how much they hated her already and the fact they would have had Sansa as the older Stark daughter already so the people who say Arya could not survive Kingslanding are right but not because Arya would not have been able to hold herself back from reacting to them but rather due to the preexisting enmity and reduced protection from her status.